17. Probabilistic Robustness Analysis of an Actively Controlled Structure that Operates in Harsh and Uncertain Environments

This work uses probabilistic robustness techniques to show how the stability margin of an uncertain controlled structure that operates in a harsh, potentially radioactive environment can be analyzed in order to find a less conservative destabilizing uncertainty perturbation. The uncertainty is quantified in terms of a measure on the size of the covariance matrix in a multivariate Gaussian distribution. This uncertainty is used to capture the aggregate effects on a structure’s dynamic behavior due to material changes resulting from radiation embrittlement and mechanical fatigue. A probabilistic-robust full-state feedback \({\mathcal {H}_\infty }\) controller is synthesized for a low-dimensional structural model using a technique known as scenario-based probabilistic-robust synthesis. A probabilistic-robust stability margin is defined and extracted from a stability degradation function, demonstrating that a fourfold increase in the amount of uncertainty in the model can be tolerated if the designer is willing to concede a small probability that the actively-controlled structure may be unstable for certain system configurations.